To find the shortest time interval for the man to cross the river, he should swim at a direction that is perpendicular to the river's flow. This way, the effective speed across the river is the difference between his swimming speed and the river's flow speed.

Given:
- Man's swimming speed in still water: 4 km/h
- River's flow speed: 3 km/h
- Width of the river: 3 km

1. Time taken to cross the river:
The effective speed across the river is the square root of (4^2 - 3^2) = 5 km/h (using Pythagoras' theorem).
Time = Distance / Speed = 3 km / 5 km/h = 0.6 hours = 36 minutes.

2. Horizontal distance traveled:
The horizontal distance traveled by the man is the same as the width of the river since he swims perpendicular to the river's flow.
Horizontal distance = Width of the river = 3 km.

So, the time taken to cross the river is 36 minutes, and the horizontal distance traveled by the man is 3 km.